Graphics Background size in relation to room size?

Hope you had a good christmas. Quick question; say for example my camera view is 512 x 288 but my room size is bigger. How do I make my 512 x 288 background fit without stretching and making the background look stretched? Do I need to make a background for each different sized room? Could I just draw the background to stay in view?

Background can tile. And you should tile them. Basically it will infinitely scroll if need be.
You don't make a background the size of a room, you will end up with a crappy background being reduced and wasted by the texture page size. Way too big asset.

Per example, in The Life Ruby my view is already 800x450 so my backgrounds are just a little larger and taller than that but they scroll if need be.

I usually make infinite-scroll backgrounds but make them bigger than 1x1 screens, to make it less obvious they're repeating (which can really make them look dead and flat). Especially natural stuff like skies and mountains are irregular, so they need to reflect in a bigger distance between tilings... indoor areas like houses can be just fine with a 64x64 texture being repeated over and over, though, because that's how real houses look.